In the history, it was Hausdorff, Berstein and Widder first studied CM functions. The 1946 book of Widder [1]} is a very good repository on this topic. The log-convexity theorem can also be found therein (p. 167). Besides, Widder also introduced the inequalities induced by the Hankel determinant. FinkHere is an error in my previous paper [2]} on the reference on the log-convexity theorem. [3]} defined a majorization relation on CM functions and established a set of inequalities including the log-convexity.
